This topic summary covers Knowledge Organiser: Conditional Probability within Conditional Probability for GCSE Mathematics. Revise Conditional Probability in Probability for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 5 of 5 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Conditional Probability
Key Terms
- Conditional probability: The probability of A given that B has already occurred
- P(A|B): Read as "probability of A given B"
- P(A ∩ B): The probability that both A and B occur
- Reduced sample space: Restricting outcomes to only those where condition B is true
- Given condition: The event after the | symbol that is known to have happened
Must-Know Facts
- P(A|B) is read "probability of A given B"
- The condition (B) becomes your new sample space — only consider outcomes where B is true
- P(B) must be greater than 0 for the formula to work
- Conditional probability is used on the second branch of a tree diagram
- In two-way tables: use the row/column total as the denominator
- The result is still a probability — must be between 0 and 1
Key Formulas
- P(A|B) = P(A ∩ B) ÷ P(B)
- P(A ∩ B) = P(B) × P(A|B)
- From a table: P(A|B) = (count of A and B) ÷ (total count of B)
Common Mistakes
- Wrong denominator: P(A|B) is conditional on B — divide by P(B), not the total probability
- Confusing P(A|B) with P(B|A): These are different — order matters in conditional probability
- From a two-way table: The denominator is the row or column total for the given condition, not the grand total
- Independent events check: If P(A|B) = P(A), the events are independent — use this to verify
Practice questions for Conditional Probability
What does the notation P(A|B) mean?
P(A) = 0.4, P(B) = 0.3 and P(A ∩ B) = 0.12. Using conditional probability, determine whether A and B are independent events. You must show all your working and give a reason for your conclusion.
Quick recall flashcards
What is conditional probability?
The probability of one event occurring given that another event has already occurred. It restricts the sample space to only the outcomes where the condition is met.
What does the vertical bar | mean in P(A|B)?
It means 'given that'. P(A|B) is read as 'the probability of A given B'. The event after the bar is the condition — it is already known to have occurred.